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Research Papers

Modeling Interparticle Size Effect on Deformation Behavior of Metal Matrix Composites by a Gradient Enhanced Plasticity Model

[+] Author and Article Information
Rashid K. Abu Al-Rub1

Mahmood Ettehad

 Zachary Departments of Civil Engineering, Texas A&M University, College Station, TX 77843,

1

Corresponding author.

J. Eng. Mater. Technol 133(4), 041015 (Oct 20, 2011) (7 pages) doi:10.1115/1.4004702 History: Received April 13, 2011; Revised June 14, 2011; Published October 20, 2011; Online October 20, 2011

Experimental tests show that particle (inclusion or precipitate) size and interparticle spacing, besides volume fraction, have a considerable effect on the macroscopic mechanical response of metal matrix microreinforced composites. Classical (local) plasticity models unlike nonlocal gradient enhanced plasticity models cannot capture this size dependency due to the absence of a material length scale. In this paper, one form of higher-order gradient plasticity enhanced model, which is derived based on principle of virtual power and laws of thermodynamic, is employed to investigate the size effect of elliptical inclusions with different aspect ratios based on unit cell simulations. It is shown that by decreasing the particle size or equivalently the interparticle spacing (i.e., the spacing between the centers of inclusions), while keeping the volume fraction constant, the average stress–strain response is stronger and more sensitive to the inclusion’s aspect ratio. However, unexpectedly, decreasing the free-path interparticle spacing (i.e., the spacing between the edges of inclusions perpendicular to the principal loading direction) does not necessarily lead to largest strengthening. This is completely dependent on the plastic strain gradient hardening due to distribution and evolution of geometrically necessary dislocations that depend on the particle size and shape. Gradient-hardening significantly alter the stress and plastic strain distributions near the particle-matrix interface.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

An SEM image of the microstructure of a structural steel showing different level of dispersed small elliptical particles [2]

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Figure 2

The plane stress unit cell model for an elliptical particle. (a) Assumed periodically arranged reinforcement in the overall inhomogeneous material. (b) The unit cell used for modeling is shown with the finite element mesh.

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Figure 3

Simulation results for L0=10 μm and a0/a0b0b0=1 showing contours of von Mises stress (in MPa) in (a) and (b); effective plastic strain in (c) and (d); and density of GNDs (in 1/m2 ) in (e) at 5% applied strain level. Here (a) and (c) show results from classical plasticity theory (i.e., for ℓ=0), while (b), (d), and (e) show results from the current gradient plasticity theory.

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Figure 4

Overall average stress–strain responses predicted by classical (L0/L0ℓℓ→∞) and gradient plasticity models for different interparticle spacing L0=40,20,10μm and different inclusion’s aspect ratio at the same particle volume fraction

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Figure 5

Simulation results for L0=10 μm and a0/a0b0b0=3 showing contours of von Mises stress (in MPa) in (a) and (b); effective plastic strain in (c) and (d); and density of GNDs (in 1/m2 ) in (e) at 5% applied strain level. Here (a) and (c) show results from classical plasticity theory (i.e., ℓ=0), while (b), (d), and (e) show results from the current gradient plasticity theory.

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Figure 6

Simulation results for L0=10 μm and a0/a0b0b0=6 showing contours of von Mises stress (in MPa) in (a) and (b); effective plastic strain in (c) and (d); and density of GNDs (in 1/m2 ) in (e) at 5% applied strain level. Here (a) and (c) show results from classical plasticity theory (i.e., ℓ=0), while (b), (d), and (e) show results from the current gradient plasticity theory.

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